COVID-19 Herd Immunity (Dec. 28, 2020)

Note: I am not a medical doctor, but I do have a Ph.D. in mechanical engineering and tend to analyze things in a logical and mathematical way. My musings and opinions below can be read with interest but should not be used to make any personal decisions regarding your health or regarding anyone else’s health. I encourage you to consult your doctor before doing anything that affects your health, and this article should not be a substitute for that.

The latest estimates show that about 0.2-0.3% of people that get COVID-19 will die, with a recent estimate of 0.27% (that continues to decline slightly). For this simplicity, in this analysis I will use a value of 0.25 which assumes that 1 in 400 people who contract COVID-19 will die from directly from COVID-19.

As of Christmas Eve, according to the Worldometers website, there were about 337,066 reported COVID-19 deaths. Multiplying the number of deaths by 400 (above I established that 1 in 400 people die directly from COVID-19) means that there are 134.83 million Americans that have had COVID-19 (or at least sufficient exposure to develop antibodies). I call this the “actual” number of cases as opposed to the number of reported cases which is 19.11 million. We know that the actual number of cases is a multiple of the reported number of cases because many people do not experience symptoms, do not report symptoms, etc.

Since there are about 331.0 million Americans and 134.83 million cases, that means that 40.7% of Americans have gotten COVID-19 (I call that the “actual case percentage” and is simply the number of actual cases divided by the population). These numbers will be important for what I discuss below.

Another value we can compute is the ratio of actual cases to reported cases. Dividing the 134.83 million actual cases by the 19.11 million reported cases, produces a ratio of 7.06. This means that, for every reported case, there are 7.06 times that number of actual cases.

Now, herd immunity typically occurs when 70-80 percent of the population has gotten the disease or are immune to it or not exposed to it. NIAID Director Anthony Fauci has recently said that it may require 90 percent to achieve herd immunity with COVID-19, though he has stated different percentages on various occasions. Herd immunity occurs when the transmission rate is very low, but actual cases (and reported cases) will start to fall when the transmission rate falls below 1.0.

Here, I think it is important to note that there are at least three ways that individuals can be "effectively immune" to COVID-19: a) by being sufficiently exposed to COVID-19 to have anti-bodies, which is what I call the number of actual cases herein; b) by receiving a vaccination that produces anti-bodies; or c) by sufficiently quarantining, masking, and/or social distancing so that one is extremely unlikely to contract the virus. This latter possibility often goes unnoticed but is important for computing the effective or statistical herd immunity of a population. For example, if the combination of wearing masks, social distancing, and quarantines were 100% effective, and if 90% of the population practiced this, then we would (effectively) already be at the 90% level for herd immunity. Thus, wearing masks, social distancing, and quarantines add some level to the herd immunity of a population.

In the case of COVID-19, presently about 3/4 of Americans use a mask regularly and over 93% use a mask at least some of the time. While masks are hardly a foolproof barrier, they do offer some resistance to the spread of COVID-19, especially when combined with social distancing. In an NPR article that quotes a meta-study by University of Washington's Institute for Health Metrics and Evaluation, if 95% of people wear cloth masks when around others, transmission is reduced by at least 30%. With that in mind, the immunity level in America is larger than the 40% provided by the actual number of cases because of the level of masks, social distancing, and even quarantining. I propose that this can be added to the level of actual cases (while subtracting the joint percentage of those that have statistically had COVD-19 and wear masks) to produce an actual percentage of the population that is “effectively” immune to COVID-19 (I recognize that there is the possibility of getting COVD-19 twice but so far that is relatively rare, and thus I am assuming most all the actual cases can be counted as part of the herd immunity).

That now begs the question: “What actual case percentage is really required to achieve herd immunity?” Several weeks ago, I mused to myself that all mitigation measures (such as the use of the masks, social distancing, etc.) must make a sizeable contribution toward effective herd immunity, and I estimated that contribution to be 20-40 percent. The study quoted above states that the mask/social distancing contribution is at least 30 percent. If we add that 30+% contribution to the 40% of the population that are already immune, we have an effective immunity level that is presently at least 70 percent. As noted above, since herd immunity typically occurs when an effective immunity level reaches 70-80 percent, this means we should start seeing some effects of herd immunity soon, or even now. This is without even considering the potential effects of a vaccine. Below I show examples that indicate that we are indeed experiencing the beginnings of herd immunity.

The proximity of various states to effective herd immunity varies state by state because the COVID-19 case and death percentages vary state by state. Some states have higher death rates than others, and thus the multiplier for obtaining actual case numbers from deaths will be different from 400 for many states. For example, one must also account for the death rate being much higher at the beginning of COVID-19. Thus, states in the northeast (like NY and NJ, along with other states that had high initial death rates, such as Louisiana and Washington) have a ratio of deaths to actual cases that is probably somewhat lower than 400.

In states with a high initial death rate, it is difficult to estimate the number of actual cases using their total number of deaths. For those states, I think that it is more accurate to estimate the actual number of cases by multiplying the number of reported cases by 7.06 (a ratio that was established earlier in this post) rather than use the 400x death multiplier method. Thus, for states that had a high death rate early in pandemic, it is more accurate to compute the actual case numbers using a multiple of the report number of cases. For states that did not experience an early pandemic breakout, it is more accurate to use the number of deaths to compute the actual case numbers (in many cases, both methods will produce a similar result).

To summarize these relationships:

For early pandemic states: Actual cases = Reported Cases multiplied by 7.06

For most states: Actual Cases = Deaths multiplied by ~400

Actual Case Percentage = Actual Cases divided by Population

Going through the states individually, when states have about 40% of their population that have had COVID-19 (actual cases), then the number of reported cases should start to drop. And sure enough, that appears to work well. States like Iowa, South and North Dakota, Illinois, Michigan, New Mexico, etc. are all seeing falling case numbers, while other states are seeing increasing case numbers. The figure below presents the 7-day moving average of reported cases for Iowa through December 24, 2020 and is similar to other states that appear to have hit the beginning of herd immunity.

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Now examining states that had high initial death rates (New York, New Jersey, etc.), we see that, despite their high death rates, using the methodology above reveals that most of these states have an actual case percentage that is only about 20-30 percent of their population. Consequently, most all of the states that had high case and death numbers early in the pandemic still have an increasing number of cases. Rhode Island is a state in the northeast that is an exception (with over 50% actual cases), but their reported number of cases appears to have recently peaked and begun to fall. Indiana, with an actual case percentage of just over 40%, has reported cases that have not fallen, but have just recently peaked, and serves as the only example I could find of the remaining states that had an actual case percentage of over 40% of their population without a significant decrease in reported cases. Unfortunately, my own state of Texas has an actual case percentage of 36% and cases are still rising (but showing signs of leveling off).

It is important to realize that the 40% actual case rate is just a ballpark estimate and the level of actual cases at which reported cases begins to decrease will vary state by state. Factors affecting the actual case percentage of the population that results in decreasing cases include the level of urbanization, the quality of health care especially early in the pandemic, race, and probably a few factors that no one has thought of. Also, it should be noted that deaths lag cases and thus the 40% level is probably off by a few percentage points.

Nationally, we are at an actual case rate of 40% of the US population, but that includes some states that had early high death rates and some that did not. Nevertheless, it appears that the number of cases nationwide is beginning to peak (and perhaps even declining, though the reporting of cases and deaths during weekends and holidays is often inconsistent). I expect that we may have some bumps up and down over the next few weeks and months (specifically one should expect a post-Christmas bounce), but we should be seeing a general decline. The figure below is the 7-day moving average for all the US. Note that, even disregarding data from December 21-24, this figure indicates that US cases are peaking.

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The addition of vaccination should somewhat accelerate the case decline. With that in mind, this article is by no means meant to discourage people from getting a vaccine or for anyone to let their guard down. The statistics show that our immunity percentage based on actual cases is at 40% and we must get to somewhere in the 70-90 percent range to see true herd immunity. We can get there by increased actual cases/deaths, masking/social distancing/quarantining as noted herein, or by vaccinations. It is our choice, but personally I prefer the latter two.

So, my point, which appears to be supported by the data, is that the combination of about 40% of the US population having already been sufficiently exposed to COVID-19 combined with masking, social distancing, quarantining, etc. means that we are already hitting the beginnings of herd immunity. If we keep doing what we are doing, then the worst will soon be behind us (though COVID-19 will still linger for at least a few more months as we march towards true herd immunity). Vaccines (and I think it is a personal decision to get a vaccine and not something that should be mandated), and the use of masks and social distancing, can accelerate our progress towards ultimate herd immunity.


Below are a few more words on some controversial subjects. Again, these are just my own views, but they appear to be well supported by data and case studies.

MASKS: In this article, I have assumed/agreed above that masks provide some level of effectiveness in combating COVID-19. It is not simply a matter of do they “work” or not, rather to what level are masks effective. They are not 100 percent effective (otherwise we would have reached effective herd immunity long ago), but they can certainly inhibit the transmission of COVID-19. There have been some excellent articles written on the subject, but suffice it to say that, with a Ph.D. in mechanical engineering with an emphasis on fluid mechanics, and as one who has studied flow through porous media in detail, masks most certainly inhibit the spread of COVID-19. Don’t believe me? Put your hand about 12 inches in front of your face and blow towards it as hard as you can. Now put a good cloth mask on and do the same thing. Of course, you will feel less air pressure from blowing on your hand. The same thing happens when you breathe, cough, sneeze, etc. – the mask inhibits the outward flow velocity and thus, if you have COVID-19, it will also inhibit the outward flow of COVID-19 particles. I perfectly understand that ,when you breathe in and out, the particles are going somewhere regardless, but they are staying closer to your body and thus are less likely to travel in large concentrations to someone else near you over a given amount of time (it is generally agreed that the time of exposure also figures into the effectiveness of masks). It is that simple. With that in mind, masks should be combined with social distancing, and reducing your time near others, to minimize your exposure.

IMMUNITY: One of the main reasons that COVID-19 affects older adults more than younger adults is because, on average, the immune system of older adults is not as strong as that of younger adults (in fact, the death rate for younger adults and children is remarkably low, which is something often overlooked). I do not believe that enough has been said by public leaders, media outlets, and healthcare authorities about this point and, more importantly, how one can strengthen their immune system. The immune system is complex, and so is strengthening it, but there are some healthy things you can do to strengthen your immune system. These include eating right, getting good sleep, reducing stress, losing weight, and getting plenty of vitamins (and probably zinc) into your system. In particular, getting sunshine and increasing your vitamin D has been shown to provide COVID-19 inhibition benefits. Since many of us have fewer reasons to get out of the house, we may be missing out on our usual supply of vitamin D more than we realize. Personally, I also gargle with mouthwash once a day. I mentally noted back in March that mouthwash should inhibit COVID-19 in the body and a recent study indicates that mouthwash may indeed be beneficial. I include this to hopefully be of benefit to the reader.

Thank you to Mitchell Allen for his review of this post.

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